How do you expand #log_3((uv^2)/w)#?

1 Answer
Tony B
May 17, 2016

So #log_3((uv^2)/w) -> (log_3(u)+2log_3(v))/log_3(w)#

Explanation:

If source values are multiplied the logs are added
#" " log(ab) -> log(a)+log(b)#

Is source values are divided the logs are subtracted.
#" "log(a/b)->log(a)-log(b)#

If source values are raised to some power then the log is multiplied by the value of the power
#" "log(a^4)->4log(a)#

If source value are rooted then the log is divided by the value of that root
#" "log(root(5)(a))-> 1/5log(a)#
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

So #log_3((uv^2)/w) -> (log_3(u)+2log_3(v))/log_3(w)#

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